Question

a bike rental costs $2.50 per hour plus a fee for renting a helmet. the total cost of renting a bike for 2 hours (h) is $13. the total cost, y, is a function of the hours, x. rate of change: 2.5 point on the graph: (2, 13) write the equation of the function. bike rentals $2.50 per hour (additional fee for helmet rental)

Explanation:

Step1: Identify the function type

The cost function is linear, so we use the slope - intercept form \(y = mx + b\), where \(m\) is the rate of change (slope) and \(b\) is the y - intercept (helmet fee). We know \(m = 2.5\) (cost per hour) and a point \((x,y)=(2,13)\).

Step2: Substitute values into the formula

Substitute \(m = 2.5\), \(x = 2\), and \(y = 13\) into \(y=mx + b\):

$$13=2.5\times2 + b$$

Calculate \(2.5\times2=5\), so the equation becomes \(13 = 5 + b\).

Step3: Solve for \(b\)

Subtract 5 from both sides: \(b=13 - 5=8\).

Step4: Write the final equation

Now that we have \(m = 2.5\) and \(b = 8\), the equation of the function is \(y = 2.5x+8\).

Answer:

\(y = 2.5x + 8\)